Wget is very powerful. There are many options, but they're not
particularly difficult to understand, so you'd be well advised to
familiarize yourself with them. The "--help" output is over 100 lines
long.

You can suppress the creation of directories based on the host name and
the leading directory components of the URL by giving wget the "-nd"
option. You can suppress the host-name directory with "-X" and you can
also have a leading sequence of some number of URL directory components
with "--cut-dirs=number".

You can get rid of URL query elements and, basically, totally override the
output file name with the "-O" option, though this is only really useful
for single-file retrievals, for the most part since it will concatentate
the retrieved data from all specified URLs into that file.

> I've tried every option in man and in the online manual.

Really? There are dozens of them!

In general, it's a good idea to quote long arguments like those typical
with wget (or to escape the special characters such as '*', '?', '[',
']', '{', '}', spaces and so on), though the likelihood that a glob
character would lead to a match with something on your system is remote.